The tertiary creep and necking of creep damaging solids

Tertiary creep and necking of bars composed of creep damaging material are investigated subject to the condition of constant applied load. The creep-damage constitutive model employed in the study is based on the concept of constrained cavity growth which characterizes the phenomenon of grain boundary cavitation in polycrystalline metals under creep conditions. For a perfect bar, tertiary creep arises from the interaction of cavitation with the geometrical effect of uniform thinning of the area cross section. Two coupled differential equations governing the evolution of the axial strain and area cross section are obtained and solved for the case of linear strain dependent nucleation. Necking is analyzed by considering the deformation of an initially imperfect bar modelled as a series of disk elements. The governing equations are integrated in these elements subject to the approximation that stresses and strains remain uniform throughout the deformation. Results indicate that the mechanism of cavitation can significantly affect the creep response of both the perfect and imperfect bars.